Singular quasilinear elliptic systems in RN\mathbb{R}^N

The existence of positive weak solutions to a singular quasilinear elliptic system in the whole space is established via suitable a priori estimates and Schauder's fixed point theorem

On a Dirichlet problem with (p,q)(p,q)-Laplacian and parametric concave-convex nonlinearity

A homogeneous Dirichlet problem with $(p,q)$-Laplace differential operator and reaction given by a parametric $p$-convex term plus a $q$-concave one is investigated. A bifurcation-type result, describing changes in the set of positive solutions as the parameter $\lambda>0$ varies, is proven. Since for every admissible $\lambda$ the problem has a smallest positive solution $\bar u_{\lambda}$, both monotonicity and continuity of the map $\lambda \mapsto \bar u_{\lambda}$ are studied.Comment: 12 pages, comments are welcom

How does a bicycle work? A new instrument to assess mechanical reasoning in school aged children

This study demonstrated that a brief interview can reveal the mechanical reasoning that could not be assessed via the Bicycle Drawing Test. This study, conducted on 190 children (6 to 11 years old), shows that mechanical reasoning improves with age. It shows correlations with spatial reasoning and motor control, and with visual reasonin

Some recent results on singular p-Laplacian equations

A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions. An extensive bibliography is also provided

Multiple Solutions to (p,q)-Laplacian Problems with Resonant Concave Nonlinearity

Abstract The existence of multiple solutions to a Dirichlet problem involving the ( p , q ) ${(p,q)}$ -Laplacian is investigated via variational methods, truncation-comparison techniques, and Morse theory. The involved reaction term is resonant at infinity with respect to the first eigenvalue of - Δ p ${-\Delta_{p}}$ in W 0 1 , p ⁢ ( Ω ) ${W^{1,p}_{0}(\Omega)}$ and exhibits a concave behavior near zero